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# Discrete Mathematics | Types of Graphs MCQs

**Discrete Mathematics | Types of Graphs MCQs**: This section contains multiple-choice questions and answers on Types of Graphs in Discrete Mathematics.

Submitted by Anushree Goswami, on July 27, 2022

**1. Graphs with _____ vertices are called null graphs?**

- Odd
- Even
- Pendant
- Isolated

**Answer:** D) Isolated

**Explanation:**

Graphs with isolated vertices are called null graphs.

**2. ____ graphs contain unordered pairs of vertices in the edge set?**

- Directed
- Undirected
- Multi
- Null

**Answer:** B) Undirected

**Explanation:**

Undirected graphs contain unordered pairs of vertices in the edge set.

**3. In a graph, ____ refers to edges that can connect the same vertices over more than one edge?**

- Multigraph
- Directed graph
- Connected Graph
- Disconnected Graph

**Answer:** A) Multigraph

**Explanation:**

In a graph, multigraph refers to edges that can connect the same vertices over more than one edge.

**4. Graphs with multiple _____ are called multigraphs?**

- Edges
- Loops
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

Graphs with multiple edges or loops are called multigraphs.

**5. Directed graph is also known as -?**

- Connected graph
- Digraph
- Disconnected graph
- Monograph

**Answer:** B) Digraph

**Explanation:**

Directed graph is also known as digraph.

**6. An edge in the _____ graph G has a direction and is identified by an ordered pair of vertex values (u, v), where u is the first vertex and v is the last vertex?**

- Connected
- Directed
- Undirected
- Disconnected

**Answer:** B) Directed

**Explanation:**

An edge in the directed graph G has a direction and is identified by an ordered pair of vertex values (u, v), where u is the first vertex and v is the last vertex.

**7. G=(V,E) is an _____ graph with n vertices where every vertex is connected to every other vertex?**

- Undirected Complete
- Directed Complete
- Undirected Incomplete
- Directed Incomplete

**Answer:** A) Undirected Complete

**Explanation:**

Explanation: G=(V,E) is an undirected complete graph with n vertices where every vertex is connected to every other vertex.

**8. How many edges are there in a complete graph with n vertices?**

- n (n - 1) / 2
- n / 2
- n (n + 1) / 2
- n (n - 1)

**Answer:** A) n (n - 1) / 2

**Explanation:**

There are n (n - 1) / 2 edges in a complete graph with n vertices.

**9. ____ graphs contain a path between any vertex u and vertex v?**

- Disconnected
- Connected
- Incomplete
- Complete

**Answer:** B) Connected

**Explanation:**

Connected graphs contain a path between any vertex u and vertex v.

**10. When there is __ path between two vertices in a graph, it is called disconnected?**

- No
- One
- Two
- Multiple

**Answer:** A) No

**Explanation:**

When there is no path between two vertices in a graph, it is called disconnected.

**11. If a subgraph of graph G is not contained in a bigger connected subgraph of G, then it is called the _____ of G?**

- Connected component
- Disconnected component
- Complete component
- Incomplete component

**Answer:** A) Connected component

**Explanation:**

If a subgraph of graph G is not contained in a bigger connected subgraph of G, then it is called the connected component of G.

**12. ____graphs G = (V, E) have n vertices and are connected by arrows between their vertices?**

- Undirected complete
- Directed complete
- Undirected connected
- Directed connected

**Answer:** B) Directed complete

**Explanation:**

Directed complete graphs G = (V, E) have n vertices and are connected by arrows between their vertices.

**13. In a graph G, the ____ is a graph that has the same number of vertices as G, but only connects two vertices that are not related to one another?**

- Supplement
- Complement
- Alternate
- None of the above

**Answer:** B) Complement

**Explanation:**

In a graph G, the complement is a graph that has the same number of vertices as G, but only connects two vertices that are not related to one another.

**14. If the edges of a graph G=(V, E) are labeled with some ____, it is called a labeled graph?**

- Name
- Data
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

If the edges of a graph G=(V, E) are labeled with some names or data, it is called a labeled graph.

**15. When each edge of graph G=(V, E) contains a positive number w, it is called a ____ graph?**

- Directed
- Complementary
- Labeled
- Weighted

**Answer:** D) Weighted

**Explanation:**

When each edge of graph G=(V, E) contains a positive number w, it is called a weighted graph.

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